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distr6 (version 1.5.2)

Quartic: Quartic Kernel

Description

Mathematical and statistical functions for the Quartic kernel defined by the pdf, $$f(x) = 15/16(1 - x^2)^2$$ over the support \(x \in (-1,1)\).

Arguments

Super classes

distr6::Distribution -> distr6::Kernel -> Quartic

Public fields

name

Full name of distribution.

short_name

Short name of distribution for printing.

description

Brief description of the distribution.

Methods

Public methods

Method pdfSquared2Norm()

The squared 2-norm of the pdf is defined by $$\int_a^b (f_X(u))^2 du$$ where X is the Distribution, \(f_X\) is its pdf and \(a, b\) are the distribution support limits.

Usage

Quartic$pdfSquared2Norm(x = 0, upper = Inf)

Arguments

x

(numeric(1)) Amount to shift the result.

upper

(numeric(1)) Upper limit of the integral.

Method cdfSquared2Norm()

The squared 2-norm of the cdf is defined by $$\int_a^b (F_X(u))^2 du$$ where X is the Distribution, \(F_X\) is its pdf and \(a, b\) are the distribution support limits.

Usage

Quartic$cdfSquared2Norm(x = 0, upper = 0)

Arguments

x

(numeric(1)) Amount to shift the result.

upper

(numeric(1)) Upper limit of the integral.

Method variance()

The variance of a distribution is defined by the formula $$var_X = E[X^2] - E[X]^2$$ where \(E_X\) is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.

Usage

Quartic$variance(...)

Arguments

...

Unused.

Method clone()

The objects of this class are cloneable with this method.

Usage

Quartic$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Details

Quantile is omitted as no closed form analytic expression could be found, decorate with FunctionImputation for numeric results.

See Also

Other kernels: Cosine, Epanechnikov, LogisticKernel, NormalKernel, Sigmoid, Silverman, TriangularKernel, Tricube, Triweight, UniformKernel